Download int_vs_sum_for_mr.mw

Looking at the attached worksheet,

it appears that the absolute value, minus 1/2, of the integral of (-1)^x*x^(1/x) from 1 to infinity would equal the partial sum of (-1)^x*x^(1/x) from 1 to where the upper summation is even and growing without bound [0]. Is anyone interested in improving or disproving this conjecture? 

As of today, March 1, 2008, I see many uploaded mw files in the Recent Files section, do not appear intact. Is anyone trying to fix that problem?

 Here is an interesting look at the tetrations (infinitely repeating powers) of some fractions.

As a side note, we see that infinitely repeating powers of 1/4 could equal one product of repeating powers of 1/16

. Download 565_multi powers 2.mw

http://www.mapleprimes.com/files/565_multi%20powers%202.mw

This blog is the second extension of MRB Constant. On May 8, 2012 I replaced some missing parts of this blog.

Some Numerical Qualities Part 1 Please, do not expect me to rehash what I have learned from books, at school or anything from the external links (or refferences to books) that have already been posted in this blog. I intend to write only that which comes from personal investigation,...